﻿\begin{tabular}{l}
\text{\LARGE{Discrete distribution}}\\
\\\hline\\
\text{Discrete probability distribution can be described by given set of all possible values}\\
\text{of the random variable with corresponding probabilities of their occurences.}
\\\\\hline\\
\text{\Large{Input parameters}}\\
    \begin{array}{ll}\\
    \\X & \text{random variable for which the set of possible values is given}\\
    \\P\left(X\right) & \text{corresponding probabilities for each value}\\
    \end{array}
\\\\\hline\\
\text{\Large{Output parameters}}\\
    \begin{array}{ll}\\
    \\\text{Expected value} & \mathbf{\operatorname{E}[X] = \mu = x_1p_1 + x_2p_2 + \dotsb + x_kp_k = \frac{x_1p_1 + x_2p_2 + \dotsb + x_kp_k}{p_1 + p_2 + \dotsb + p_k}}\\
    \\\text{Standard deviation} & \mathbf{\sigma = \sqrt{\sum_{i=1}^N p_i(x_i - \mu)^2}}\\
    \\\text{Variance} & \mathbf{\sigma^2 = \operatorname{Var}(X) = \sum_{i=1}^n p_i\cdot(x_{i} - \mu)^2 = \sum_{i=1}^n (p_i\cdot x_{i}^2) - \mu^2}\\
    \end{array}
\end{tabular}